Find the conditional distribution of X given Y = y Find the conditional expectation of X given Y = y Find the conditional variance of X given Y = y
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First, we need to find the conditional distribution of X given Y = y, which is represented as P(X | Y = y). Show more…
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Show that the variance of the conditional distribution of $Y$, given $X=x$, in Exercise 2.5.3, is $(1-x)^{2} / 12,0<x<1$, and that the variance of the conditional distribution of $X$, given $Y=y$, is $y^{2} / 12,0<y<1$.
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Show that the variance of the conditional distribution of $Y$, given $X=x$, in Exercise $2.20$, is $(1-x)^{2} / 12,0<x<1$, and that the variance of the conditional distribution of $X$, given $Y=y$, is $y^{2} / 12,0<y<1$.
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